Scanning tunneling microscopy has been a powerful tool in expanding our understanding in the study of condensed matter physics. Many of the exotic materials of interest exhibit rich phases of matter at different temperatures and pressures. In order to probe the rich array of phases we developed a novel technique of combining scanning tunneling microscopy with tunable temperature and tunable mechanical strain in ultra high vacuum conditions. The mechanisms that give rise to high temperature superconductivity has been a long standing problem in physics. The discovered of iron-based high temperature superconductors (pnictides) have spurred much research into the mechanisms that give rise to the different exotic states observed in these new materials in hopes to better understand the underlying nature of unconventional superconductivity. Here we present a detailed study of the Nematic ordered phase in the prototypical iron- based high temperature superconductor, NaFeAs. Using our novel strain, temperature, scanning tunneling microscopy technique, we can attain an atomic-resolution view of the effects of the nematic phase on the local density of states along with the effects of anisotropic strain on the electronic structure. We further systematically study NaFeAs along both axes of the phase diagram, tuning temperature and Cu doping. We probe the material from the parent compound to beyond the supercon- ducting dome with increased Cu doping and from superconducting temperatures towell above the structural transition temperatures. Using our novel strain, temperature, scanning tunneling microscopy technique we nanoscopically identified the region of long-range nematic order and the region of nematic fluctuations in the phase diagram and find that true long range nematic order sets in at the tetragonal to orthorhombic structural transition temperature but nematic fluctuations continue at higher temperatures and also into the overdoped regime, then seemingly disappearing at the edge of the superconducting dome. We further find that our applied stain increasing the amplitude of the nematic fluctuations showing strong nonlinear coupling between strain and electronic nematicity. The power of our novel strain, temperature, scanning tunneling microscopy tech- nique in probing quasiparticle interference proves ideal for studying the topological, Weyl semimetal 1T’-MoTe 2 . In it’s orthorombic phase the material has topologically nontrivial protected surface Fermi arcs. By measuring quasiparticle interference in this material at different temperatures we can probe both topologically nontrivial phase (orthorhombic phase) and the topologically trivial phase (monoclinic phase). In the topologically nontrivial phase we see quasiparticle interference measurements in good agreement with angular resolved photoemission spectroscopy and theoretical calculations. In the topologically trivial phase we see the lack of the quasiparticle interference coming from the trivial surface state.

This thesis investigates the use of single Cooper-pair transistor (SCPT) for fast and sensitive detection of quasiparticle dynamics. This investigation is motivated by the possibility of quantum information processing using superconducting nanoscale circuits, such as the SCPT and the Cooper-pair-box (CPB). In the SCPT coherent charge transport can be temporarily halted due to quasiparticle tunnelling, known as quasiparticle poisoning. Quasiparticle poisoning can be reduced by the use of engineered island and lead gap energies. The thesis begins by reporting measurements of the superconducting gap in aluminium - aluminium-oxide - aluminium tunnel junctions, as a function of film thickness. We have observed an increase in the superconducting energy gap of aluminium with decreasing film thickness. This method is used to engineer the island and gap energies in a SCPT and consequently we observe reduced poisoning and a modification of the thresholds for finite bias transport processes. Radio-frequency reflectometry is used to perform high-bandwidth measurements of quasiparticle tunnelling in a gap engineered SCPT. A model for the radio-frequency (rf) operation of the SCPT is presented and shows close agreement with experiment. Thermal activation of the quasiparticle dynamics is investigated, and consequently, we are able to determine energetics of the poisoning and unpoisoning processes. This enables an effective quasiparticle temperature to be determined, allowing the poisoning to be parametrised. An investigation of the use of normal metal quasiparticle traps for suppression of quasiparticle poisoning in SCPT devices is performed. To date, there has been little quantitative information about the behaviour of quasiparticle traps even though they have been used extensively. The work presented serves to clarify the nature of quasiparticle trap performance. Finally the single-quasiparticle sensitivity of the SCPT is employed to directly probe a few quasiparticle gas in a small superconducting volume. The quasiparticle population is monitored both in the steady-state and under non-equilibrium conditions of injection. In the non-equilibrium regime the quasiparticle recombination time is accessed from the response of the SCPT to pulsed injection. Agreement to previous experimental studies of recombination times in aluminium is found.

This thesis investigates the use of single Cooper-pair transistor (SCPT) for fast and sensitive detection of quasiparticle dynamics. This investigation is motivated by the possibility of quantum information processing using superconducting nanoscale circuits, such as the SCPT and the Cooper-pair-box (CPB). In the SCPT coherent charge transport can be temporarily halted due to quasiparticle tunnelling, known as quasiparticle poisoning. Quasiparticle poisoning can be reduced by the use of engineered island and lead gap energies. The thesis begins by reporting measurements of the superconducting gap in aluminium - aluminium-oxide - aluminium tunnel junctions, as a function of film thickness. We have observed an increase in the superconducting energy gap of aluminium with decreasing film thickness. This method is used to engineer the island and gap energies in a SCPT and consequently we observe reduced poisoning and a modification of the thresholds for finite bias transport processes. Radio-frequency reflectometry is used to perform high-bandwidth measurements of quasiparticle tunnelling in a gap engineered SCPT. A model for the radio-frequency (rf) operation of the SCPT is presented and shows close agreement with experiment. Thermal activation of the quasiparticle dynamics is investigated, and consequently, we are able to determine energetics of the poisoning and unpoisoning processes. This enables an effective quasiparticle temperature to be determined, allowing the poisoning to be parametrised. An investigation of the use of normal metal quasiparticle traps for suppression of quasiparticle poisoning in SCPT devices is performed. To date, there has been little quantitative information about the behaviour of quasiparticle traps even though they have been used extensively. The work presented serves to clarify the nature of quasiparticle trap performance. Finally the single-quasiparticle sensitivity of the SCPT is employed to directly probe a few quasiparticle gas in a small superconducting volume. The quasiparticle population is monitored both in the steady-state and under non-equilibrium conditions of injection. In the non-equilibrium regime the quasiparticle recombination time is accessed from the response of the SCPT to pulsed injection. Agreement to previous experimental studies of recombination times in aluminium is found.

Thesis (Ph. D.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 13, 2006) Vita. Includes bibliographical references.

For over a decade now there has been much research into the use of superconductors in X-ray, gamma ray and other particle detectors. Detectors based on superconductor-insulator-superconductor(SIS) and superconductor-insulator-normal metal(SIN) tunnel junctions have been widely developed. To date, the predicted excellent energy resolving ability of such detectors has not been realised. Various energy loss processes have been suggested as possible causes for the failure to obtain energy resolutions close to the thermodynamic and quantum limits predicted. In my experiments, I have used both SIS and SIN tunnel junctions to investigate the transport of quasiparticles and phonons in structures similar to the proposed detector designs. I have used multiple distributed junction geometries to perform injection-detection type experiments. One junction is used to inject quasiparticles and/or phonons into the device structure, whilst the current-voltage characteristic of a second junction is monitored for a response to the injected quasiparticles/phonons. Using this type of experimental set-up, I have measured the transport of non-thermal equilibrium quasiparticles in an epitaxial niobium film. Using a simple random walk model, I have calculated an effective lifetime for quasiparticles. I have not observed the process of quasiparticle mulitiplication that has been observed by other researchers - I attribute this to differences in the microstructure of my devices and comment on the implications of this to possible quasiparticle loss mechanisms. I have investigated the energy transport in a device with a number of SIN tunnel junctions connected to a common normal metal electrode. Phonon transport via the substrate is found to be the dominant coupling process between the tunnel junctions, although the device design can result in some junctions being effectively shielded from the substrate phonons by the common electrode. Finally, the possibilities of using a superconducting heterostructure to control the rate at which quasiparticles recombine and emit phonons have been explored. Excessive recombination is believed to limit the effectiveness of large areas SIN tunnel junctions as thermometers for particle detecting bolometers.

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Abstract not available

Thesis (Ph.D.)--Mississippi State University. Department of Physics & Astronomy. / Title from title screen. Includes bibliographical references.

The Schrödinger equation is nearly a century old, yet we are still in the midst of uncovering the remarkable phenomena emerging in many-body quantum systems. From superconductivity to anyonic quasiparticles, nature consistently surprises with its rich self-organization. To elucidate and grasp this variety, it is paramount to understand the phases of matter that can occur in many-body ground states, as well as their emergent collective excitations. Of particular interest are topological phases of matter, characterized by exotic excitations or edge phenomena. There exist by now several universal frameworks for gapped systems, i.e., those with an energy gap above the ground state. However, in the last decade, a multitude of gapless quantum wires---effectively one-dimensional systems---have been reported to be topologically non-trivial. A framework for their understanding and classification is missing. In addition to ground state order---topological or otherwise---a more complete picture involves the properties of excitations above the ground state. Alas, little is known about excitations beyond the universal low-energy regime. In part, this is due to a lack of analytical and numerical methods able to describe excitations at finite energies, especially in strongly-interacting systems beyond one dimension. In this thesis, we address these issues: firstly, we build a general understanding of topological phases in one dimension, including both gapped and gapless cases. In particular, we unify previously studied examples into a single framework. Secondly, we develop a novel numerical method for obtaining spectral functions in two dimensions---these give direct insight into the properties of excitations and are moreover experimentally measurable. Using this numerical method, we uncover a variety of robust properties of excitations at finite energies. Part I of this thesis concerns gapped and gapless topological phases in one dimension. In Chapter 2, we first treat the case of non-interacting fermions. Therein, we review the known classification of gapped phases before extending it to the gapless case, showing that exponentially-localized Majorana zero modes can still emerge at the edge when the bulk is gapless. Interacting gapped phases are discussed in Chapter 3, with a focus on symmetry-protected topological order. These have already been classified; our contribution is to provide a non-technical review of this classification as well as showing that many paradigmatic model Hamiltonians can be related to one another. Finally, Chapter 4 introduces the notion of symmetry-enriched quantum criticality, which we propose as a framework for classifying gapless phases. The key message is that in the presence of symmetries, a universality class can divide into distinct phases, characterized by the symmetry action on the low-energy scaling operators. This includes gapless topological phases, with examples hiding in plain sight; we clarify their stability and reinterpret previously studied examples. Part II studies the excitations above the ground states of two-dimensional quantum spin models. The main object of our study is the dynamic spin structure factor; this type of spectral function is reviewed in the first part of Chapter 5. The second part of this chapter introduces a novel matrix-product-state-based algorithm to efficiently compute it, opening a new window on the dynamics of two-dimensional quantum systems. We benchmark this numerical method in Chapter 6 on the exactly-solvable Kitaev model---a paradigmatic topological model realizing a quantum spin liquid. By adding non-integrable Heisenberg perturbations, we identify the first unequivocal theoretical realization of a proximate spin liquid: the ground state becomes conventionally ordered, yet the high-energy spectral properties are structurally similar to those of the nearby Kitaev spin liquid. The latter agrees with aspects of recent inelastic neutron scattering experiments on alpha-RuCl3. In Chapter 7, we turn to one of the oldest models in many-body quantum physics: the spin-1/2 Heisenberg antiferromagnet on the square lattice. Despite its venerable history, there is still disagreement about the physical origin of high-energy spectral features which low-order spin wave theory cannot account for. We provide a simple picture for this strongly-interacting-magnon feature by connecting it to a simple Ising limit. Lastly, Chapter 8 discusses the stability of quasiparticles---collective excitations behaving like a single emergent entity, of which magnons are a prime example. These are often known to be stable at the lowest energies and are presumed to decay whenever this is seemingly allowed by energy and momentum conservation. However, we show that strong interactions can prevent this from happening. We numerically confirm this principle of avoided decay in the (slightly-detuned) Heisenberg antiferromagnet on the triangular lattice. Moreover, we can even identify its fingerprints in existing experimental data on Ba3CoSb2O9 and superfluid helium. In this thesis, we thus enlarge our understanding of quantum phases and their excitations. The identification of the key principles of gapless topological phases in one dimension calls for direct analogues in higher dimensions, waiting to be uncovered. With regard to the robust properties of the excitations identified in this thesis, we are hopeful that these can be extended into a theory of quasiparticle properties away from the universal low-energy regime.

We reserve the first part of this thesis to a brief (and by far incomplete, but hopefully self-contained) introduction to the vast subject of quantum Hall physics. We dedicate the first chapter to a discursive broad introduction. The second one is instead used to introduce the integer and fractional quantum Hall effects, with an eye to the synthetic quantum matter platforms for their realization. In the third chapter we present famous Laughlin's wavefunction and discuss its basic features, such as the gapless edge modes and the gapped quasiparticle excitations in the bulk. We close this introductory part with a fourth chapter which presents a brief overview on the chiral Luttinger liquid theory. In the second part of this thesis we instead proceed to present our original results. In the fifth chapter we numerically study the linear and non-linear dynamics of the chiral gapless edge modes of fractional quantum Hall Laughlin droplets -- both fermionic and bosonic -- when confined by anharmonic trapping potentials with model short range interactions; anharmonic traps allow us to study the physics beyond Wen's low-energy/long-wavelength chiral Luttinger liquid paradigm in a regime which we believe is important for synthetic quantum matter systems; indeed, even though very successful, corrections to Wen's theory are expected to occur at higher excitation energies/shorter wavelengths. Theoretical works pointed to a modified hydrodynamic description of the edge modes, with a quadratic correction to Wen's linear dispersion $\omega_k=vk$ of linear waves; even though further works based on conformal field theory techniques casted some doubt on the validity of the theoretical description, the consequences of the modified dispersion are very intriguing. For example, in conjunction with non-linearities in the dynamics, it allowed for the presence of fractionally quantized solitons propagating ballistically along the edge. The strongly correlated nature of fractional quantum Hall liquids poses technical challenges to the theoretical description of its dynamics beyond the chiral Luttinger liquid model; for this reason we developed a numerical approach which allowed us to follow the dynamics of macroscopic fractional quantum Hall clouds, focusing on the neutral edge modes that are excited by applying an external weak time-dependent potential to an incompressible fractional quantum Hall cloud prepared in a Laughlin ground state. By analysing the dynamic structure factor of the edge modes and the semi-classical dynamics we show that the edge density evolves according to a Korteweg-de Vries equation; building on this insight, we quantize the model obtaining an effective chiral Luttinger liquid-like Hamiltonian, with two additional terms, which we believe captures the essential low-energy physics of the edge beyond Wen's highly successful theory. We then move forward by studying -- even though only partially -- some of the physics of this effective model and analyse some of its consequences. In the sixth chapter we look at the spin properties of bulk abelian fractional quantum Hall quasiparticles, which are closely related to their anyonic statistics due to a generalized spin-statistics relation - which we prove on a planar geometry exploiting the fact that when the gauge-invariant generator of rotations is projected onto a Landau level, it fractionalizes among the quasiparticles and the edge. We then show that the spin of Jain's composite fermion quasielectron satisfies the spin-statistics relation and is in agreement with the theory of anyons, so that it is a good anti-anyon for the Laughlin's quasihole. On the other hand, even though we find that the Laughlin’s quasielectron satisfies the spin-statistics relation, it carries the wrong spin to be the anti-anyon of Laughlin’s quasihole. Leveraging on this observation, we show how Laughlin's quasielectron is a non-local object which affects the system's edge and thus affecting the fractionalization of the spin. Finally, in the seventh chapter we draw our conclusions.